Abstract
Consider a tree T and a forest F. The paper discusses the following new problems: The Forest vertex-cover problem (FVC): cover the vertices of T by a minimum number of copies of trees of F, such that every vertex of T is covered exactly once. TheForest edge-cover problem (FEC): cover the edges of T by a minimum number of copies of trees of F, such that every edge of T is covered exactly once. For a solution to always exist, we assume that F contains a one vertex (one edge) tree.
Two versions of Problem FVC are considered: ordered covers (OFVC), and unordered covers (UFVC). Three versions of Problem FEC are considered: ordered covers (OFEC), unordered covers (UFEC) and consecutive covers (CFEC). We describe polynomial time algorithms for Problems OFVC, UFVC and CFEC, and prove that Problems OFEC and UFEC are NP-complete.
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Gavril, F., Itai, A. (2009). Covering a Tree by a Forest. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_7
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DOI: https://doi.org/10.1007/978-3-642-02029-2_7
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